Direct observation of twisted stacking domains in the van der Waals magnet CrI3

Van der Waals (vdW) stacking is a powerful technique to achieve desired properties in condensed matter systems through layer-by-layer crystal engineering. A remarkable example is the control over the twist angle between artificially-stacked vdW crystals, enabling the realization of unconventional phenomena in moiré structures ranging from superconductivity to strongly correlated magnetism. Here, we report the appearance of unusual 120° twisted faults in vdW magnet CrI3 crystals. In exfoliated samples, we observe vertical twisted domains with a thickness below 10 nm. The size and distribution of twisted domains strongly depend on the sample preparation methods, with as-synthesized unexfoliated samples showing tenfold thicker domains than exfoliated samples. Cooling induces changes in the relative populations among different twisting domains, rather than the previously assumed structural phase transition to the rhombohedral stacking. The stacking disorder induced by sample fabrication processes may explain the unresolved thickness-dependent magnetic coupling observed in CrI3.

Figures originally included in the author's rebuttal have been redacted from this file.

Reviewer comments:
Reviewer #3 (Remarks to the Author) In the manuscript "Direct observation of intrinsic twisted stacking domains in the van der Waals magnet CrI3" resubmitted to Nature Comms, the authors have properly addressed all the questions I raised in the previous review.The additional experiments done by the authors substantially strengthened the manuscript.The finding that exfoliation introduces much more stacking faults is interesting as well.I believe the manuscript meets the standard of Nature Communications, therefore can be published in its current form.
Reviewer #4 (Remarks to the Author) This manuscript investigates stacking domains within the monoclinic phase of CrI3 and explores their impact on magnetic properties.Through atomic resolution electron microscopy imaging of cross-sectional samples, the authors convincingly demonstrate the presence of 120° stacking domains and elucidate their dependence on thickness and sample preparation methods.Notably, the study reveals hysteric behavior in the stacking domain population during a temperature cycle.The authors argue that no magnetic contrast in Lorentz TEM data is consistent with the absence of structural phase transitions to the rhombohedral phase at low temperatures.While the stacking domains reported here offer insights into the structural phase transition in thin layers and its implications for 2D magnetism, a clear link between these stacking domains and magnetic properties remains elusive.While the electron microscopy data, including high-quality atomic images, are carefully analyzed, the manuscript lacks essential magnetic property data.Due to this deficiency, I am unable to recommend this manuscript for publication in Nature Communications.Addressing this gap would significantly strengthen the manuscript and its contribution to the understanding of 2D magnetism.
For authors' reference, an early Lorentz TEM study on CrI3 is reported by O Bostanjoglo and W. Vieweger "Low-temperature Lorentz microscopy on "weak" ferromagnetics", Phys.Stat. Sol. 32, 311 (1969).The thickness of CrI3 flake in this study is not specified but a weak stripe domain contrast is clearly shown in the ab plane sample (Figure 10).
There is a Lorentz TEM study on stacking faults in another 2D magnet, Cr2Ge2Te6.This study reports the absence of interaction between stacking faults and ferromagnetic interlayer coupling or anisotropy.The work shows similar atomic electron microscopy images of stacking faults (see Figs. 1f-j) and Lorentz TEM images (see Fig. 4f), both obtained from a cross-sectional sample.Drawing parallels between the findings in Cr2Ge2Te6 and the current investigation on CrI3 stacking domains may offer valuable comparative insights into the behavior of these 2D magnetic materials.The observed lack of interaction in Cr2Ge2Te6 suggests that stacking faults might not significantly influence interlayer magnetic coupling.

Overall comment:
In the manuscript "Direct observation of intrinsic twisted stacking domains in the van der Waals magnet CrI3" resubmitted to Nature Comms, the authors have properly addressed all the questions I raised in the previous review.The additional experiments done by the authors substantially strengthened the manuscript.The finding that exfoliation introduces much more stacking faults is interesting as well.I believe the manuscript meets the standard of Nature Communications, therefore can be published in its current form.

Response:
Thank you for your support.We really appreciate the reviewerâ s comments during the previous revision.The manuscript was significantly improved owing to the reviewerâ s insightful comments Reviewer #4 Overall comment: This manuscript investigates stacking domains within the monoclinic phase of CrI3 and explores their impact on magnetic properties.Through atomic resolution electron microscopy imaging of cross-sectional samples, the authors convincingly demonstrate the presence of 120Â° stacking domains and elucidate their dependence on thickness and sample preparation methods.Notably, the study reveals hysteric behavior in the stacking domain population during a temperature cycle.The authors argue that no magnetic contrast in Lorentz TEM data is consistent with the absence of structural phase transitions to the rhombohedral phase at low temperatures.While the stacking domains reported here offer insights into the structural phase transition in thin layers and its implications for 2D magnetism, a clear link between these stacking domains and magnetic properties remains elusive.While the electron microscopy data, including high-quality atomic images, are carefully analyzed, the manuscript lacks essential magnetic property data.Due to 1 this deficiency, I am unable to recommend this manuscript for publication in Nature Communications.Addressing this gap would significantly strengthen the manuscript and its contribution to the understanding of 2D magnetism.

Response:
We appreciate the reviewer's valuable comments and suggestions.As the reviewer acknowledged, the detailed structural study (monoclinic domains persistent down to low temperature, three variants of monoclinic domains, the domain size depending on the sample preparation methods and thickness) reported in the current manuscript provides insightful information on the layered magnetic crystals.We would like to remark that the magnetic data as mentioned by the reviewer, i.e., Lorentz TEM (LTEM), was supplemented during the previous revision.It shows that a nonferromagnetic phase is present into the samples at low temperature.Since the layers are at monoclinic phase, this is consistent with an antiferromagnetic order where no magnetic contrast can be observed in the LTEM images.Thus, this provides the missing link between structure and magnetic properties pointed out by the Reviewer.In the updated version we have made sure that this connection is clearly included.
Below we address the reviewerâ s specific comments to clarify some raised concerns.
Comment 1: For authorsâ reference, an early Lorentz TEM study on CrI3 is reported by O Bostanjoglo and W. Vieweger â Low-temperature Lorentz microscopy on "weak" ferromagneticsâ , Phys.Stat. Sol. 32, 311 (1969).The thickness of CrI3 flake in this study is not specified but a weak stripe domain contrast is clearly shown in the ab plane sample (Figure 10).
Response: Thank you very much for pointing out the relevant reference.We agree that the mentioned reference is relevant to our manuscript.We included the reference in the revised manuscript.

Changes made:
The following reference was added in the main manuscript.
In page 11, â ¦ Lorentz TEM imaging is a powerful tool to investigate the local magnetic property in samples35,36,45.Comment 2: There is a Lorentz TEM study on stacking faults in another 2D magnet, Cr2Ge2Te6.This study reports the absence of interaction between stacking faults and ferromagnetic interlayer coupling or anisotropy.The work shows similar atomic electron microscopy images of stacking faults (see 2 Figs.1f-j) and Lorentz TEM images (see Fig. 4f), both obtained from a cross-sectional sample.Drawing parallels between the findings in Cr2Ge2Te6 and the current investigation on CrI3 stacking domains may offer valuable comparative insights into the behavior of these 2D magnetic materials.The observed lack of interaction in Cr2Ge2Te6 suggests that stacking faults might not significantly influence interlayer magnetic coupling.
Response: We appreciate the Reviewerâ s comment.The mentioned paper presented results on the ferromagnetic properties and electrical transport behavior in Cr2Ge2Te6 (CGT), another important 2D magnetic crystal.However, CGT does not show any dependence of its magnetic properties with sample thickness or number of layers (e.g., ferromagnetism/antiferromagnetism for odd/even number of layer).In this aspect, CrI3 is quite unique on the relation between stacking order and magnetic coupling.Moreover, other vdW magnets (e.g., CrSBr, CrPS4) more recently have been observed to show similar layer dependence on their magnetic features similarly as CrI3.This indicates that a potential large family of layered compounds, either known or yet to be discovered, might show similar properties as the ones measured in our manuscript.Indeed, the analysis, guidelines, and arguments included in our results might provide further pathways for additional exploration for the community.We included additional discussions on other kinds of 2D magnetic crystals and comparison with CrI3 is beneficial to our manuscript.

Changes made:
To address the Reviewerâ s comment, the following discussion and reference were added in the main manuscript.
In page 11-12, â ¦ Another 2D magnetic material, such as Cr2Ge2Te6, exhibits the stacking-fault-insensitive magnetic domain structure35,36,46.The absence of various types of crystal configurations and nonstacking dependence on the magnetic properties of Cr2Ge2Te6 is in stark contrast to the CrI3 case, showcasing that the stacking configuration is indeed paramount to its magnetic ordering.Nevertheless,other compounds (CrSBr,CrPS4,MnBi2Te4)47,48,49,50 share such relationship between stacking order and magnetic coupling as that present in CrI3.This indicates that a potential large family of layered compounds, either known or yet to be discovered, might show similar properties as the ones measured here.Indeed, the analysis, guidelines, and arguments included in our results might provide further pathways for additional exploration.Comment 3: Exploring the lateral structure of stacking domains can provide valuable insights into the effects of these domains on magnetic properties.Cross-sectional imaging might not be the most effective approach for this purpose.I suggest that the authors consider acquiring dark-field TEM images of the ab plane view.Considering the electron diffraction patterns obtained from the ab plane flake in Figure S2d, dark-field TEM images with reflections from various 120Â° stacking domain variants could reveal clear lateral domain distributions and sizes.This approach would allow for a more detailed analysis of how lateral variations in stacking domains are influenced by sample preparation, thickness, and temperature.Integrating such dark-field TEM images into the study would enhance the understanding of the spatial arrangement of stacking domains and their impact on magnetic properties.

References
Response: Thank you for your valuable comments.As suggested by the reviewer, we have conducted extra experiments on the in-plane lateral domains in CrI3.Specifically, 1) we have performed dark-field TEM imaging with plan-view CrI3 samples with various thickness, and 2) observed the changes in domain structures at low-temperature (liquid N2 temperature).The added data clearly exhibit that the lateral stacking domains are the order of micrometers.Moreover, DF images from relatively thick samples shows the stripe pattern and the direction of domain boundaries is preferred along one direction.The presence of twisted domain boundary in the lateral direction results from the local stacking transition.Therefore, the formation of domain boundaries will be strongly influenced by the sliding direction possessing a lower energy barrier associated with stacking shift, and the observed preference of the domain boundary formation can be attributed to the direction of strain applied during sample exfoliation/transfer process.In addition, we directly observed that the stacking domain changes upon cooling, which also provides extra information how the switch in stacking domain occurs.As the temperature decreased from room temperature to lower temperatures, the minor domain areas decreased while the predominant domain areas increased, which is consistent with the cross-section TEM analysis in the manuscript.We believe that the provided extra experimental data significantly improve the quality of our work, and our manuscript is ready to be accepted promptly.

Changes made:
To address the Reviewerâ s comment, the following discussion and Supplementary Figures S12-14 and S16 were added.
In page 10, â ¦ DF imaging with plan-view samples was also performed to characterize the size and distribution of the twisted domains in the lateral direction.For the plan-view DF imaging, we mainly utilized mechanically exfoliated and transferred CrI3 samples as the sample fabrication directly from the bulk crystal was unsuitable.We note that the samples thicker than ~100 nm have some challenges for directly visualizing lateral domains due to the multiple-scattering during electron diffraction process and complex domain structures as the number of vertical domains grow.Supplementary Figures S12~14 show representative DF imaging data of CrI3 flakes with thickness ranging from 15 nm to 40 nm.Individual twisted domains can be identified by DF imaging by selecting relevant diffraction signals as shown in Supplementary Figure S12d~h.The total sum of intensities in three DF images overall displays the uniform intensity, consistent with the uniform intensity observed in bright field image.We found that the lateral domain size of three twisted variants is the order of micrometers as shown in Supplementary Figures S12  and S13.On the other hand, DF images from relatively thick samples shows the stripe pattern and the direction of domain boundaries is preferred along one direction as shown in Supplementary Figure S14.The presence of twisted domain boundary in the lateral direction results from the local stacking transition, and the sliding direction possessing a lower energy barrier associated with stacking shift stacking will be preferred27.
In page 11, â ¦ Temperature-dependent DF imaging of the lateral twisted domains also showed that the lateral domain population and its boundary change at low temperatures, consistent with observation of cross-sectional samples (Supplementary Figure S16)....